In Harsanyi and Selten's equilibrium selection theory, the linear tracing procedure has been used to model the hypothetical reasoning process of expectation formation. This paper reconsiders the linear tracing procedure from the perspective of the relationship between priors and Nash equilibria. A prior belongs to the source set of a Nash equilibrium if the linear tracing procedure based on this prior leads to that equilibrium. We show that for any Nash equilibrium, its source set is always nonempty and closed, but not generally convex. This paper also constructs an approach of iterative application of the linear tracing procedure to the auxiliary games that are used to model the hypothetical reasoning under the procedure. We present a notion of robustness of Nash equilibria based on this idea, by replacing uncertainty modelled by a single probability measure with uncertainty modelled by sets of probability measures. This approach attempts to capture the fact that players may not be sufficiently confident in the available information in order to single out one probability distribution that represents their initial beliefs about the other players' possible strategy choices.
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